Question: Reduce to lowest terms: $ \dfrac{6}{7} \div \dfrac{3}{5} = {?}$
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{3}{5}$ is $ \dfrac{5}{3}$ Therefore: $ \dfrac{6}{7} \div \dfrac{3}{5} = \dfrac{6}{7} \times \dfrac{5}{3} $ $ \phantom{ \dfrac{6}{7} \times \dfrac{5}{3}} = \dfrac{6 \times 5}{7 \times 3} $ $ \phantom{ \dfrac{6}{7} \times \dfrac{5}{3}} = \dfrac{30}{21} $ The numerator and denominator have a common divisor of $3$, so we can simplify: $ \dfrac{30}{21} = \dfrac{30 \div 3}{21 \div 3} = \dfrac{10}{7} $